Explain how the probability of two independent events occurring together is calculated.

Take a guess: A student takes a multiple-choice test that has 7 questions. Each question has five choices. The student guesses randomly at each answer. Let be the number of questions answered correctly. Round the answers to at least four decimal places. Part 1 of 2 (a) \( P(4)=0.0287 \) Part: \( 1 / 2 \) of 2 (b) \( P \) (More than 2\( )= \)

Take a guess: A student takes a multiple-choice test that has 7 questions. Each question has five choices. The student guesses randomly at each answer. Let \( X \) be the number of questions answered correctly. Round the answers to at least four decimal places. Part: \( 0 / 2 \)

5. Marty has exactly 5 blue pens, 6 black pens, and 4 red pens in his knapsack. If he pulls out one pen at random from his knapsack, what is the probability that the pen is either black or red?

Dos refrigeradores expostos em uma loja, um cliente esco- lheu um aleatoriamente. A probabilidade de o refrigerador escollhido ser da marca X e ser frost free é \( \frac{7}{10} \). Sabendo que a probabilidade de o escolhido ser da marca X é \( \frac{3}{5} \) e que a probabilidade de ele ser frost free é \( \frac{3}{4} \), calcule a probabili- dade de esse refrigerador ser da marca \( X \) ou ser frost free.

확률변수 \( X \) 가 정규분포 \( N\left(40,5^{2}\right) \) 를 따를 때, 확률 \( P(X \leq 50)=\alpha \) 이다. 이 때 \( 10000 \alpha \) 의 값을 구하여라.